Presents activities that can be helpful in establishing a conceptual basis for dividing rational numbers. Some activities involve metric units while others are appropriate for small-group work with calculators. (AIM)

Presents a short section from a science fiction/fantasy novel by Terry Pratchett called "The Colour of Magic." Discusses its usefulness as a read-aloud for mathematics instruction of geometry, particularly the concept of circumference. (SR)

Underlines the common points in F. Uhlig's approach published in an earlier issue of this journal about the question of proof in linear algebra. Describes some of his ideas in a new light and gives perspective for a further didactical development of Uhlig's first experiments. (Author/KHR)

Describes how mathematical understanding grows and develops while children play with the mathematical ideas they see emerging as they hear and talk about the story "Selina and the Bear Paw Quilt". (Author/NB)

Presents a case study of young children measuring on the playground to illustrate the development of understanding of units of measurement and the importance of teachers capitalizing on the informal mathematical situations that arise naturally in children's conversations. (Author/NB)

Describes probability games and tasks to help students educate their primitive intuitions connected with the concept of "fairness" in the outcomes of compound events. (YDS)

Explores differences between mathematical definitions and non-mathematical definitions by contrasting three approaches to mathematical reasoning. Examines the consequences of the use of those approaches in a first course in real analysis. Analyzes students' reasoning behavior during analysis and suggests reasons for students' difficulties with the…

Presents two methods for replacing a series by one converging more rapidly: regrouping the terms of a series and manipulations of power series. Describes a general algorithm for approximating the natural logarithm of any number. (YP)

Investigated differences in performance between sexes on a spatial visualization task constructing pentaminos and whether supplying clues to the learner to guide would be a factor in performance. Concluded that males were more adept at identifying the shapes than females. (YP)

A learning and teaching approach using base-10 blocks to embody the English named-value system of number words and digit cards to embody the positional base-10 system of numeration is described. Examines the students' understanding and arithmetic skills on the multidigit arithmetic. (Author/YP)

Presents a device for sketching the graph of the composite and inverse of single variable real-valued functions. Discusses some didactic methods of paths. (YP)

Examines whether the embodiment of a familiar geometric system facilitates better understanding of the vector-space concept than the embodiment of a variety of unfamiliar algebraic systems. Analyzes students' responses with description, final answer, and justification of answers. Provides six problems. (YP)

Claims that most of mathematical knowledge is neither as widely applicable as general heuristics, nor as narrow as the facts in textbooks and that it consists of general concepts. Describes some examples and characteristics of the general concepts. (YP)

Introduces a statistics curriculum emphasizing an instructional sequence of practical, real data, discussion, and model/theory instead of theory, example, and practice. Provides one example and describes the teaching methods of the curriculum. (YP)

The "word problem" is stated for a given collection. Facts regarding Dehn's Algorithm, definition of Thue systems, a rewriting system, lemmas and corollaries are provided. The situation is examined where the monoid presented by a finite Thue system is a group. (DC)